\relax 
\citation{Williams:78:shadowmaps}
\citation{PCF}
\citation{PCSS}
\citation{ConvolutionSoftShadowMaps2}
\citation{SummedAreaVSM}
\citation{VSSM}
\citation{VSSM}
\citation{SAT}
\citation{ESM}
\citation{ShadowSurvey}
\citation{SoftShadowSurvey}
\citation{ShadowCourseNotesSigA2009}
\citation{ShadowSTAREG2010}
\@LN@col{1}
\@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{1}}
\newlabel{sec-intro}{{1}{1}}
\@LN@col{2}
\@writefile{toc}{\contentsline {section}{\numberline {2}Related work}{1}}
\newlabel{sec-related}{{2}{1}}
\citation{AttyBP}
\citation{GaelBP1}
\citation{GaelBP2}
\citation{SchwarzBP}
\citation{GaelBP3}
\citation{PCF}
\citation{VSM}
\citation{CSM}
\citation{ESM}
\citation{VSM}
\citation{VSSM}
\citation{CSM}
\citation{ESM}
\citation{SAT}
\citation{SAT05}
\citation{SAT05}
\citation{VSM}
\citation{SummedAreaVSM}
\citation{SummedAreaVSM}
\citation{ConvolutionSoftShadowMaps2}
\citation{SummedAreaVSM}
\citation{VSSM}
\citation{ConvolutionSoftShadowMaps2}
\citation{VSSM}
\@LN@col{1}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.1}Soft Shadow Mapping via Back-projection}{2}}
\newlabel{subsec-SSM-bp}{{2.1}{2}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.2}Soft Shadow Mapping via PCSS}{2}}
\newlabel{subsec-SSM-pf}{{2.2}{2}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.2.1}Pre-filtered Hard Shadow Mapping}{2}}
\newlabel{subsec-SSM-pfhsm}{{2.2.1}{2}}
\@LN@col{2}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.2.2}Pre-filtered Soft Shadow Mapping}{2}}
\newlabel{subsec-SSM-pfssm}{{2.2.2}{2}}
\@writefile{toc}{\contentsline {section}{\numberline {3}Algorithm Overview}{2}}
\newlabel{sec-overview}{{3}{2}}
\citation{ESM}
\citation{PCSS}
\citation{SummedAreaVSM}
\citation{ConvolutionSoftShadowMaps2}
\citation{VSSM}
\@LN@col{1}
\@writefile{loa}{\contentsline {algorithm}{\numberline {1}{\ignorespaces Overview of ESSM Algorithm}}{3}}
\newlabel{ESSM_Overview}{{1}{3}}
\@writefile{toc}{\contentsline {section}{\numberline {4}Exponential Soft Shadow Mapping}{3}}
\newlabel{sec-ESSM}{{4}{3}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.1}Review of Exponential Shadow Mapping}{3}}
\newlabel{subsec-ESM}{{4.1}{3}}
\@LN@col{2}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.2}Estimating Average Blocker Depth}{3}}
\newlabel{subsec-ZAVG}{{4.2}{3}}
\citation{VSSM}
\citation{VSSM}
\citation{ESM}
\citation{VSSM}
\@LN@col{1}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.3}ESM non-planarity problem and its solution}{4}}
\newlabel{sec-ESMNP}{{4.3}{4}}
\newlabel{fig:np1}{{1(a)}{4}}
\newlabel{sub@fig:np1}{{(a)}{4}}
\newlabel{fig:np2}{{1(b)}{4}}
\newlabel{sub@fig:np2}{{(b)}{4}}
\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Comparison between the soft shadows rendered without/with kernel subdivision. (a)\hbox {}: Incorrect lit without subdivision. (b)\hbox {}: Artifact fixed with subdivision.}}{4}}
\newlabel{fig:ESSMNP}{{1}{4}}
\@LN@col{2}
\@writefile{toc}{\contentsline {section}{\numberline {5}SAT numerical problem and its solution}{4}}
\newlabel{sec-SAT}{{5}{4}}
\newlabel{fig:sat1}{{2(a)}{4}}
\newlabel{sub@fig:sat1}{{(a)}{4}}
\newlabel{fig:sat2}{{2(b)}{4}}
\newlabel{sub@fig:sat2}{{(b)}{4}}
\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces Comparison between the original SAT filtering and adaptive sub-SAT. (a)\hbox {}: Noises introduced by SAT precision loss. (b)\hbox {}: Precision saved by the adaptive sub-SAT.}}{4}}
\newlabel{fig:subSAT}{{2}{4}}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.1}Adaptive subdivided SATs}{4}}
\citation{SummedAreaVSM}
\citation{SAT05}
\citation{Sub-pixelAntialiasedShadow}
\citation{PVSSM}
\citation{PVSSM}
\citation{PVSSM}
\@LN@col{1}
\newlabel{fig:uniform}{{3(a)}{5}}
\newlabel{sub@fig:uniform}{{(a)}{5}}
\newlabel{fig:kdtree}{{3(b)}{5}}
\newlabel{sub@fig:kdtree}{{(b)}{5}}
\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces The uniform and KDTree subdivision scheme. The green squares are sub-SATs. The yellow rectangles are penumbra filter kernels. (a)\hbox {}: The uniform subdivision is efficient to be parallel implemented on GPU. The filter kernels across the sub-SAT borders are easy to handle. (b)\hbox {}: The KDTree subdivision reaches least division counts and optimal sub-SATs. But the overhead of constructing the KDTree and maintaining the data-structure to handle filter kernels across the sub-SAT borders is too expensive compared to the benefits.}}{5}}
\newlabel{fig:subSAT}{{3}{5}}
\@LN@col{2}
\@writefile{toc}{\contentsline {section}{\numberline {6}Anisotropic filtering of soft shadows with SAT}{5}}
\newlabel{sec-aniso}{{6}{5}}
\@writefile{toc}{\contentsline {subsection}{\numberline {6.1}Anisotropic anti-aliasing of soft shadows}{5}}
\@writefile{toc}{\contentsline {subsection}{\numberline {6.2}Approximate anti-aliasing kernel by subdivision}{5}}
\bibstyle{model3-num-names}
\bibdata{ESSM}
\bibcite{Williams:78:shadowmaps}{{1}{1978}{{Williams}}{{}}}
\bibcite{PCF}{{2}{1987}{{Reeves et~al.}}{{Reeves, Salesin and Cook}}}
\bibcite{PCSS}{{3}{2005}{{Fernando}}{{}}}
\bibcite{ConvolutionSoftShadowMaps2}{{4}{2008{}}{{Annen et~al.}}{{Annen, Dong, Mertens, Bekaert, Seidel and Kautz}}}
\bibcite{SummedAreaVSM}{{5}{2007}{{LAURITZEN}}{{}}}
\bibcite{VSSM}{{6}{2010}{{Yang et~al.}}{{Yang, Dong, Feng, Seidel and Kautz}}}
\bibcite{SAT}{{7}{1984}{{Crow}}{{}}}
\bibcite{ESM}{{8}{2008{}}{{Annen et~al.}}{{Annen, Mertens, Seidel, Flerackers and Kautz}}}
\bibcite{ShadowSurvey}{{9}{1990}{{Woo et~al.}}{{Woo, Poulin and Fournier}}}
\bibcite{SoftShadowSurvey}{{10}{2003}{{Hasenfratz et~al.}}{{Hasenfratz, Lapierre, Holzschuch and Sillion}}}
\bibcite{ShadowCourseNotesSigA2009}{{11}{2009}{{Eisemann et~al.}}{{Eisemann, Assarsson, Schwarz and Wimmer}}}
\bibcite{ShadowSTAREG2010}{{12}{2010}{{Scherzer et~al.}}{{Scherzer, Wimmer and Purgathofer}}}
\bibcite{AttyBP}{{13}{2006}{{Atty et~al.}}{{Atty, Holzschuch, Lapierre, Hasenfratz, Hansen and Sillion}}}
\bibcite{GaelBP1}{{14}{2006}{{Guennebaud et~al.}}{{Guennebaud, Barthe and Paulin}}}
\bibcite{GaelBP2}{{15}{2007}{{Guennebaud et~al.}}{{Guennebaud, Barthe and Paulin}}}
\bibcite{SchwarzBP}{{16}{2007}{{Schwarz and Stamminger}}{{}}}
\bibcite{GaelBP3}{{17}{2009}{{Yang et~al.}}{{Yang, Feng, Guennebaud and Liu}}}
\bibcite{VSM}{{18}{2006}{{Donnelly and Lauritzen}}{{}}}
\bibcite{CSM}{{19}{2007}{{Annen et~al.}}{{Annen, Mertens, Bekaert, Seidel and Kautz}}}
\bibcite{SAT05}{{20}{2005}{{Hensley et~al.}}{{Hensley, Thorsten, Greg, Montek and Anselmo}}}
\bibcite{Sub-pixelAntialiasedShadow}{{21}{2009}{{Pan et~al.}}{{Pan, Wang, Chen, Zhou and Bao}}}
\bibcite{PVSSM}{{22}{2011}{{Li et~al.}}{{Li, Guennebaud, Yang and Feng}}}
\@LN@col{1}
\newlabel{fig:aa1}{{4(a)}{6}}
\newlabel{sub@fig:aa1}{{(a)}{6}}
\newlabel{fig:aa2}{{4(b)}{6}}
\newlabel{sub@fig:aa2}{{(b)}{6}}
\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces Anisotropic anti-aliasing through our filter approximating. (a)\hbox {}: Naive filtering results with penumbra kernel. (b)\hbox {}: Filtering with anti-aliased soft shadow filter.}}{6}}
\newlabel{fig:aa}{{4}{6}}
\@writefile{toc}{\contentsline {section}{\numberline {7}Results}{6}}
\@writefile{toc}{\contentsline {section}{\numberline {8}Conclusions and Future Works}{6}}
\@LN@col{2}
\newlabel{fig:dino}{{5(a)}{7}}
\newlabel{sub@fig:dino}{{(a)}{7}}
\newlabel{fig:ogre}{{5(b)}{7}}
\newlabel{sub@fig:ogre}{{(b)}{7}}
\newlabel{fig:plant}{{5(c)}{7}}
\newlabel{sub@fig:plant}{{(c)}{7}}
\newlabel{fig:balls}{{5(d)}{7}}
\newlabel{sub@fig:balls}{{(d)}{7}}
\@writefile{lof}{\contentsline {figure}{\numberline {5}{\ignorespaces Shadow quality generated by ESSM, tested with different scenes. \G@refundefinedtrue {\unhbox \voidb@x \hbox {\normalfont  \bfseries  ??}}\GenericWarning  {               }{LaTeX Warning: Reference `sub@fig:dino' on page 7 undefined}: A dino scene run at 125fps. (b)\hbox {}: A complex scene run at 115fps. (c)\hbox {}: A plant scene run at 147fps. (d)\hbox {}: A large scale balls scene run at 21fps}}{7}}
\newlabel{fig:results}{{5}{7}}
